Parasound HINT vs. Bryston 135-3 or Simaudio 340i D3PX


I have a Parasound HINT integrated amp and am considering replacing it with Bryston 135-3 or Simaudio 340i D3PX. Both options are available used at about half of new retail price. I am aware that the Parsound is considered good value, and I appreciate what it does, including the useful options for managing subwoofers in both HT and two-channel applications.
For those here who are familiar with the Parsound amp and either or both of the Bryston and Simaudio integrateds, will you please tell me what I would gain with an upgrade?My listening space is a basement room, approximately 20' x 20'. I have Harbeth Compact 7es3 speakers for left and right channels, along with two Rythmik F8 subwoofers. My primary source is an Oppo UDP-205. Cables are Audience, with Furutech power distribution.
If I would do better with a speaker upgrade than a more expensive amplifier, please just say so. Thanks for your input.
conlad
Thanks to those who have responded already with different opinions to consider. 
As for desired changes or improvements, I am hoping for improved soundstage depth at least. I recently added one Furutech NCF Clear Line unit to my system, and that has improved the apparent separation of instruments and voices in the soundstage. 
I have been fortunate to acquire much of my system at reduced prices, and I have tried to prioritize value, which is a reason that I chose the Parasound HINT amp. If improving on its performance will cost far more than its price, I would rather save for a more costly upgrade than to spend money on incremental changes. 
For a speaker upgrade, I have looked at Spendor 7.2 but read that its midrange is not on par with more traditional Spendor designs. I really like the Harbeth Compact 7’s but realize that I could buy better speakers. I would rather not buy speakers that have a significantly larger footprint. I listen to jazz and rock for the most part, and I am not a basshead.  
Not everyone agrees with @stereo5 that the Bryston is bright. I have heard a couple of all-Bryston systems that were stunning. The cubed units are especially refined and NOT bright sounding. That is based on my own 4B3, and also dozens of reviews.

I have also heard some Simaudio gear, and I think it’s great, too. However, I’ve never heard the particular units you are mentioning, nor been able to compare Bryston and Simaudio in the same room with the same speakers.

The Parasound HINT is well respected, but I’ve not heard it. I’d be hesitant to buy the Bryston or Sim and expect a major change. And I don’t believe either will do subs. So perhaps you are right to be thinking about speakers as an alternative.

I suppose we should ask the obvious question: Are there particular areas of your current sound you wish to change?
Changing speakers is the way to better sound, it will be the biggest sound change, I would suggest a speaker that moves a little more air, provides a little more punch if you will,what that speaker is will be for you to hear. I would get new speakers and use that Parasound until such time that either it quits on you or you quit on it. Most speakers are going to be in the moderately sensitive range which the Parasound should be able to drive. Building a system from the Speakers back is the way to go, after all this is the part of the system you interact with the most.

Matt M
I owned a Parasound Hint and have heard the Bryston integrated.  The Parasound is better, the Bryston is bright, bright, bright!  Never heard the Sim Audio. IMHO, if you want better sound, you need to look at something much better, perhaps a Luxman or Accuphase integrated.  If you get the Bryston or Sim Audio, it will be a sideways move at best.