Critical oppositions made using inadequate equipment.

Yes, you can. I do it all the time.

I have 107 cartridges, at least that many styli that I evaluate, compare, review, and enjoy. I have 17 TTs that I mount them in with varying arm masses and configurations.

My equipment is not expensive, and hardly high end by most standards in here. 
But I can clearly hear all the subtle, nuanced, drastic differences in cartridges and styli. For set up of cartridges and styli, I listen through a $6 pair of MonoPrice headphones. They readily reveal VTF issues, alignment errors, tracking issues, distortions, and any other problems. I also make styli for several rare cartridges. 
So, yes you absolutely CAN hear differences using inexpensive (consumer grade) TTs, receivers, amps, headphones, phono preamps, cables, interconnects.  I do it and enjoy it every day.

You have to listen in your system and only your opinion is valid when you choose a component. I bought far more turntables than I actually need, too many tonearms, and many more cartridges of all types (some very rare units). Different phono stages, SUTs, headamps ... Some people have more, some are totally insane in this hobby.

I also adjust and test every new cartridge not in the main system, I use headphones and two identical turntables to test carts, styli etc, I can immediately switch between two identical turntables. I can hear the difference using professional Sennheiser HD-25 headphones. For the first teste it’s enough.

I got 3 pairs of speakers and they are vary from bookshelf professional Tannoy monitors to the huge main Tannoy monitors and floorstanding high-end speakers. I have couple of friends with nice systems and we can meet for a listening session. Everywhere we can hear the difference, but I enjoy the most my MAIN system, this is where I use only the best and every change in that system is audible (cable, phono stage, tonearm, cartridge... whatever).

@mijostyn

We all have our own ideas of what is best.

I’m totally agree on this one. No dogma exists in our hobby. At some point you just start to understand that you ready for your own concepts and whoever suggesting to you or gives you some strong opinions are  basing on their own, probably weak experience and maybe even wrong understanding. 

"Maybe even wrong understanding."   The biggest  issue I see with the out spoken people is there lack of experience  with live real music.  They always fall back on detail and pump up highs.  They use the terms  air around instrument , black background,  neutral,   sound stage,  etc etc ...  In all the posts did anyone ask you what your goal is.  What are you looking for.  What is your  musical  background.?  What music do you listen to?  Etc Etc ...  

Is the tone, body, timbre, pitch of acoustical  instruments important  to you?  Is the attack and decay of interest.  How loud and what size room do want to fill with music.  Do you want to feel like  you are at a rock concert,  classical  auditorium,   Or a  small jazz club with out big ass studio monitors  to mess things up.    

In regards to real music the mid range is where at least 80% of the action is.  Studio monitors  can be the best here.  Rodgers and Spendor 3/5  monitors  are superb.   Of course Quads and some planar are great mid range speakers also.  

So to your original question,  it would be hard to answer not knowing what you like and want from music.  If detail is your thing  there is plenty  of solid state amps and speakers to let you hear changes in carts and table arm combos.  If going for the Holy Gail  of real Live music , where vinyl  is King ,  things get more complicated.   Here I would go down the tube stuff ave which would cost more but really sounds like the real deal.  The hardest  part is knowing the weak component is with out knowing your goals.  If you are truthly looking for a answer  for your journey  then I would define your goals  then get the speakers  to get you close , then amps that can make them sing.  Then fine tune them with table/arm/ cartridge. 

Enjoy the ride
Tom