Have a U-Turn turntable with Ortofon 2M Red cartridge. Upgrade cartridge or turntable???

Ortofon 2M Red cartridge that was included. The Ortofon cartridge is good but is sounding worn; and, therefore am considering a Denon 110 high output MC cartridge which will work with this table.

High Output MC is bad idea, if you want an MC look for LOMC or leave the idea buying an MC (if you don’t have MC phono stage) and stick with MM or MI (they are better at this price and stylus is user replaceable).

What is the budget for a cartridge alone (without turntable) ?

If you have $350-450 for a cartridge then look for Stanton 881s mkII or Pickering XSV/3000SP .... these are the best performers you can get for the money. Both with Stereohedron stylus profile. Pickering XSV/3000-SP optimized for modern mid mass tonearms. 

If the budget is lower i don’t really know what to say.

@chakster I'm not sure why you keep recommending cartridges that aren't in production and nearly impossible to find.  

You'll get more bang for the buck upgrading the turntable.  Consider buying used.  Try going a little higher in the Music Hall line, like a MMF-7X or 5X.  I haven't heard the Classic, but it looks like a decent enough table if you prefer to buy new.  It should be an incrememtal step up.

You might be able to find a decent used table with an OK cartridge at your budget and then you can upgrade the cartridge later.

If the turntable itself has issues adding a better cartridge won't make them go away.  I'd rather put an inexpensive cartridge on a good turntable than a good cartridge on an inexpensive turntable.  It all matters, but the turntable is the foundation.

How long have you had the cartridge?  

I am not a fan of the U-Turn table, but I am not sure I would go for a Music Hall either. There isn't anything about it that stands out that defines it as a quality turntable. Personally? I would find a nice demo, open box, or even pre owned Rega and start with that. If you went pre owned I would budget in an upgrade for a Tango sub platter in the future and you would have a nice bang for the buck table. 

As far as the Denon cartridge goes, I would think that is a fine upgrade over the Ortofon Red. The Red is a polarizing cartridge, there are many people who find it too aggressive and unrefined. The 110 is a tried and true budget cartridge, with a good quality diamond on it for the price. If you shop carefully on the net it can be had for under $300. It being HOMC is not a bad thing, while LOMC is technically better, there are many well built HOMC cartridges out there, the Denon is one of them. One caveat though. Its output level is not as strong as many MM or MI cartridges, so be prepared to have to turn the volume up a bit higher than what you currently do. 

Other cartridge alternatives are from the Audio Technica line. The VM540ML is getting good feedback from owners. I also hear of folks taking the 95 body and putting the LP Gear Vividline stylus on it and getting very nice sound for the money. These are good choices also. 

But audio is an adventure! There are many pathways to good sound, and all of us have different things we want to hear. Best of luck with your journey.