Yeah, I find the pad on the DS4 to be particularly uncomfortable. These games have become a lot more pad friendly, but I think even if you were using a comfortable one a stick is going to be a lot more comfortable in long play sessions.
The TE2+ is very easy to open, but the HRAP4 isn't even remotely hard to mod either. You can just use a phillips head screwdriver and open it up from the bottom. The TES+ doesn't look like it would be hard to open, but I do not know for sure, for what it's worth I am buying a TE2+ but you could probably save the $30 on that end if you really want to.
If you haven't owned a stick before and you don't know what type of parts you prefer the HRAP4 is the better bet. The TEs all have Sanwa JLF sticks and the HRAP4 has a Hori Hayabusa, which one of those you'll prefer is just a personal preference, the buttons are also mainly preference but I think the Sanwa are a bit higher quality durability-wise from what I've read (I prefer a Seimitsu LS-32 and buttons personally so I'm swapping out regardless).
Basically the long and short of it is that the two sticks are roughly equal in quality with thier stock parts so unless you have a preference for the Sanwa parts and know it you're better off with the HRAP4 as it will save you $50 (Which is about the price difference in swapping the parts so even if you decide you like Sanwa or Seimitsu you're even). If you prefer Sanwa and know it the Madcatz will save you the (Admittedly small effort) in switching