While we often consider a card's value to be the top priority when trading, there are many other factors that should be considered. These factors include immediate need/want, speculative potential, format playability, collectability (perhaps you collect a certain card or artist), difficulty of acquiring or replacing a different copy, buy-list value and ease of unloading.
Many of these factors are almost subconsciously answered before the trade even starts. For some examples let's say the following offers are made (assume NM condition for all cards involved).
Pile 1 ($25.32 TCG Mid)
Pile 2 ($24.98 TCG Mid)
From a pure numbers standpoint pile 1 is more valuable. Both cards see play in Modern and Legacy and could easily be considered staples.
Now, decide which pile you'd prefer to have.
I can see the trade from both sides. If I have pile 1 I'm trading three lower-value cards for a higher-value card which has seen only one printing. The amount of money I'm losing is minimal compared to the fact that I'm consolidating into a more valuable asset.
If I have pile 2, on the other hand, I'm splitting up an expensive asset into three cheaper assets that are worth slightly more money. Any gains by the Blood Moon I'll see three-fold compared to any gains in the Catacombs. I'm expecting the Modern metagame to use even more non-basics than currently and this card just showed up as a 4-of in a Legacy deck that did well at GP Strasbourg.
How about another one:
Pile 1 ($125.22 TCG Mid)
Pile 2 ($124.9 TCG Mid)
Again from a pure numbers standpoint pile 1 is more valuable, but not by much. But this time we have a high-dollar legacy staple crucial to a top tier deck compared to a Legacy/Modern-legal fetchland. Both have only one printing (though the Catacombs was included in an event deck). Now, which pile would you prefer to have? Again, I can see the trade from both sides.
Pile 1 is unloading some high dollar Legacy cards seen in only 1-2 decks. There's a possibility of the card getting banned which would tank it's value. I can trade into an asset that has a strong demand due to its playability across multiple formats.
Pile 2 is consolidating into more valuable assets that are the backbone of a tier 1 Legacy deck.
Breaking Down the Factors
Now that we have the exercise out of the way let's look into some of the factors we used to judge those trades.
When you need a card (for a tournament or a deck you've always wanted to build) you'll often value it higher than normally. Even knowing the current value, you'll still be willing to part with a little bit more than you would for a card of equal value that you don't "need." This is knowledge you would prefer your trading partner not know as this gives them the edge. If you needed one of those piles in order to play in a tournament that started in 10 minutes you'd process the trade differently and most likely be willing to give up the most in trade.
This category is a bit more difficult to conceptualize, but it's easier when you tie it with "collectability". Let's say you collect Serra Angels and you run into someone with a 7th Edition foil in Japanese. This isn't a card you'll see often and while it's by no means one of a kind, you could easily go for years without seeing another in a trade binder. You want this card, you feel as though you need it, but it's not for a deck.
You can keep your desire for the card a bit more under wraps because you don't have an immediate time factor. You might try to show some interest and if the owner seems unwilling to budge wander off and catch up with them later in the hopes that they are more willing to negotiate as the day has worn on and few people have shown any interest in it. You still don't want to leave the tournament site without owning this card, but you can hold back a bit to get a better deal.
This is a factor we are all familiar with. When you believe the future value of a card will rise from its current value you subconsciously assign that card more value in your head. Not that you'll tell your trade partner, but if you can come to a close deal you don't mind gaining less value or losing a small bit because you've already decided the card is more valuable than it's current price indicates.
This is a strong factor for many of us because the upside can be tremendous. As we have seen, Magic cards can double or triple in a matter of days and the elation of catching the cards before the spike is tremendous.
This concept describes how good a card is in relation to how often it can be in demand, due to the range of formats in which it is played. A perfect example is Liliana of the Veil. Currently she's played in Legacy, Modern and Standard, the trifecta for traders. Demand for her is high and is expected to remain so due to her playability across all formats. The more formats a card is playable in the higher the expected demand and the more stable the price (though in this context stable often means less likely to drop as it could still spike upwards).
This is a look at how desirable the card is from a collector's standpoint. The best examples are often Angels or Dragons, which tend to maintain a higher price point than another card that is exactly the same, but of a different creature type (this price isn't always all that significant, but it's still something to consider).
Ease of Replacement
When I trade off Legacy cards I often consider how difficult it would be for me to get the card back, not out of fear of "trader's remorse", but simply because some cards you rarely see in trade binders. Ironically, this doesn't always directly correlate to the card's value. Some of my favorite examples are Yawgmoth's Will and Vampiric Tutor, cards I rarely see in any trade binders but which are both are less than $30.
This is a great way to trade when your plan is to sell cards to buylists. You can trade cards that are of equal value but buylist at different values. This works well when the cards you have buylist for less but are highly in demand. On a side note it's also critical to compare buylist values as stores will change their buylist based on the demand they are seeing (and demand can vary based on location).
Ease of Unloading
I factor this in when picking up higher dollar cards that are difficult to trade. Sometimes it's difficult to trade off some high dollar Legacy staples that see limited play. For example, The Tabernacle at Pendrall Vale and Moat are both $300+ dollar cards but finding a buyer/trader is difficult because they are typically only played in one or two decks.
The good news is that if you're looking for one of these you can often get them undervalued if you have high-velocity cards to trade for them. A great example: I traded for an english NM Moat (that was hand-painted) for 1x Volcanic Island-NM (Revised), 1x Badlands-HP (Unlimited), 4x Steam Vents (RTR), 2x Grove of the Burnwillows. The guy mentioned that people commented on the Moat all day but nobody wanted it. He was happy to get rid of it and I got it for about $75 off because it was altered (despite the fact that it looks gorgeous).
Last but not least, the most obvious factor is the card's actual value. While this can often differ by what source you use, when trading most people default to this factor and while they may consider some of these other factors this is the one they latch onto. One important strategy I use is when people ask you what you put the card at, I give a range. This is critical to keep from getting pigeon-holed by sharks. If a card is $8 on TCG-Mid and $10 on SCG saying $7-10 works well because it gives you leverage when your trade partner starts pricing their cards.