A basic 28-300 (equiv.) "walk-around lens" on an APS-C SLR or a high quality fixed lens on a 1" sensored bridge camera? Let's say
Nikon D3300 w/
Tamron 18-200 f/3.5-6.3 vs. Panasonic
FZ1000 with its 25-400 lens at 28, 50, 100, 200, and 300mm equivalents. Assume the same resolution output file.
Would I be wrong in assuming that the built-in lens of the FZ is higher quality than the Tamron?
If not, is the lens better enough to make up for the much smaller sensor?
I often discourage the walk-around lenses on the basis of low optical quality, compared to primes or narrower zooms. Now, I'm second-guessing myself.
+1 Second guess yourself!

LOL.
I'm just wondering if someone who buys an APS-C SLR with an ultrazoom lens and just leaves it on is really better served than someone with a smaller-sensored camera with a superior lens.
I am one of those people.
When on vacation, I'll take my Nikon D5100 and just have my Nikon 18-135mm f3.5-5.6 superzoom. And for when it gets dark, I have my Nikon 35mm f1.8 lens. That's pretty much it.
But I have had a Sigma 18-200mm f3.5-6.3 superzoom on my Pentax K100d as well as a Promaster 18-200mm f3.5-6.3 superzoom (which I believe was a rebadged Tamron) on my Nikon D70s.
And if you get those lenses enough light, they can really bang out a great picture.
Here are some shots I took with those lenses way back when, when I was 1st getting into off camera flash . . .
As a measuring stick, let's also be realistic here: Assume image is compressed and viewed on a typical 21" monitor. Which would look better, or would we be unable to tell?
But besides just optics . . . to me there are other things to take into consideration.
Things like . . . how quick can you get to the focal length you want. How fast does the camera focus. How short is the trigger delay? And things like that.
Heck. As an experiment, I once shot a cheerleading routine with my Nikon D5100 with my Nikon 18-135mm f3.5-5.6 lens. I had to up the auto-iso to max iso6400. And use aperture priority since my aperture was changing. But the camera was able to keep up. Zooming was manual, so I got to the focal length I wanted to be at quickly. Focus was fast. (cheerleading has lots of light at bigger events). And trigger delay was very, very small. So I walked away with 20-30 shots from a < 2 min routine.
And right after that I did the same thing with my Tamron 28-75mm f2.8 lens. The benefit of using the constant aperture lens was that I was able to peg iso at iso3200 and leave it there. And I was able to set aperture and shutter speed up and forget it, so no surprises from the camera. And I think that helps to squeeze a bit more IQ out of the camera.
When I looked at the images on-screen, both were great. Both were completely usable! Of course, when I pixel peeped, I could just make out some distortion on the 18-135mm lens. But I really had to go looking for it.
Here is one of the cheerleading shots taken with my Nikon D5100 and my Tamron 28-75mm f2.8.
But besides all that . . . the benefit of an interchangeable lens camera is that when you want to . . . you can change the lens to something that suits what you are shooting.
Although I don't do a lot of it, I do have a macro lens . . .
https://www.flickr.com/photos/tacticdesigns/4697290897/in/dateposted-public/
And being able to slap on a constant aperture lens, such as my Tamron 28-75mm f2.8 or Nikon 80-200mm f2.8 lens can IMHO really go a long way to getting the shot.
https://www.flickr.com/photos/tacticdesigns/18703668855/in/dateposted-public/
https://www.flickr.com/photos/tacticdesigns/15528608821/in/dateposted-public/
As for your Nikon D610. Maybe that Nikon 24-120mm f4 lens would be a good fit. I so wanted to get it when I got my D750, but it was completely out of my budget.
Take care & Happy Shooting!
