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Well, first of all, remember that it's effective stacks that matter.
The main advantage of playing deep is that you get more implied odds. You're a better player, so when you beat your opponents at showdown, it's going to be for more money (unless you're not a better player, in which case you need to get off the table).
You might be more inclined to 3bet light, or cold call with suited connectors, though remember, you're still mainly looking to take the pot away often enough to make it worth while; the implied odds are just a bonus.
If you call someone who's 160BB deep with you, raising 4BB and you think you can get them all in 1 time out of 40, win every time you do, and fold otherwise, it's a break even move to call them. Added to that you will be winning smaller pots on occation, either at showdown, or by bluffing, think about calling with suited gappers, and suited connected aces, against players who are likely to get it all in post flop, or play weakly.
Having said all this, there's no shame in leaving if you think you no longer have an edge over the table. If I see a good player come to my table, I leave. There's nothing I can do about that, but you can get used to playing deep. Maybe go to Stars NL2 for a few thousand hands - it's 250BB deep. You do want to get over this, because what you're doing now is leaving any table you beat.
Personally, if I'm at a table, it's because I think I'm better than it, and if I think I'm better than it, I want the most money possible in front of me.
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