I think this is something that only you can answer... its personal choice really.
Theres plenty of 3.7s on here that are lifted, just as I'm sure there's people who make their 3.7s more street...
You're gonna be investing money into it either route you go..and youre probably gonna drop a little MPGs as well... do you think that's something youre okay with doing?
If it is, would you like your jeep to be modded for the outdoors and offroading, or more for street performance?
I dont know a lot about going the street route, but I would imagine you would need to invest quite a lot in terms of engine mods to get it up to par, unless you want to have it just look street, but not perform that way...which IMO, i dont see the practicality in that..but like you mentioned.. I may be a little bias. You'll also have your other mods like springs and shocks and struts, tires, wheels and exterior mods.
If you want to go the offroad route.. you'll be investing in a lift, struts, shocks, tires, and any exterior mods you want as well.. and you'll be loosing a little MPGs with bigger tires.. (you'll probably lose em though too with the street route)
After having a toyota corolla handed down to me since I was 17, I decided to buy a jeep as soon as I had the money at 23.. I went the offroad route bc I like the outdoors and wanted to take my jeep where I couldnt go with the corolla and even with the 4.7 v8 in my WK, I lost some MPGs (3 to be exact)..but I'm okay with that.. bc I bought jeep, not another corrolla.
Its ultimately your decision.. based on purely what kind of driving you like to do and your decision if its worth it to pay to add onto what you have now...
do you love your jeep to the point where you know youre gonna have it for some time still and want it a certain way? then do it! however which route you take... or maybe you're looking to trade it soon... maybe you decide not to pour money into it then.. and if you go with another jeep, perhaps decide its more worth it to mod a newer(to you) jeep down the line that is more capable with its base specs..
If you decided to lift your current jeep..overall a good guess on what would happen is.. you'd be dropping $3K and losing 3-5MPGs.. can't really speak for the street jeeps..
I think the great thing about jeeps is their versatility.. if you're gonna mod..decide if its worth investing in the current jeep you own, make it fit your lifestyle and I'm sure you'll be happy.