Most Joysticks (even non-HOTAS) need both hands to operate:
One hand at the stick, one hand at the base of the stick to avoid slipping.

How would you play if you need both hands to use the stick? Unless the stick has enough buttons and such that you can use it as a standalone controller...
Thoughts: (disclaimer: I've never tried either of the sticks you mentioned)
If you're planning on playing for quite a while (more than several months; note the many mods and TCs released and in progress), and willing to pay slightly outside your price range, the CH Flightstick Pro is
currently available for $57 on Amazon. CH Products has an excellent reputation for the build quality/durability of their products and their customer service/support, but the Flightstick Pro's big disadvantages are that it has relatively few buttons (although enough for space sims IMO) and that it doesn't have a "twist" for the roll axis like the Logitech stick does (I improvise by using the hat switch). Their more expensive sticks have a lot more buttons and such but are well outside your price range, they also don't have a twist, and for me at least, they're too big for my hands. Another nice plus of the Flightstick Pro is that DOSBox (a DOS emulator that Good Old Games uses a lot) has built-in support for it, so if you ever decide to get, say,
Descent from GOG, setup is really easy, and the stick really does make Descent a lot more fun.
But between the two sticks you're considering, I'd go with the Logitech one, for the reasons you mentioned (PS3 control images would be a turn-off to me, too

), and I figure the fewer features it has (stick vs HOTAS), the fewer things that can break.

My impression from the reviews is that Logitech's quality control is iffy, so be sure to hold onto the receipts/packaging in case you get a defective one and have to exchange it.
Honestly, when it comes to cheap joysticks, you probably get what you pay for, in the long run at least. But the Logitech stick sounds like it's what you're looking for. Just be aware that it's unlikely to continue working well in the long run (or possibly even short run).
Other thoughts: (don't you just love unsolicited advice?

)
If you've just been playing for a couple days, you might want to wait a bit -- say, a week or two or more -- before deciding whether to shell out the money for a joystick. A lot of people are happy with just a keyboard or maybe keyboard and mouse. I have a HOTAS (CH Flightstick Pro + CH Pro Throttle) and I still use the keyboard from time to time.
Hope that helps.