The later Vixen Porta mount is so much better that the old-style Vixen Custom mount. (That is what Vixen called that alt-az mount in your top picture, the ‘Custom’ mount. Here’s my trusty Vixen Porta II that I’ve had around 10 years. It’s a very good mount. I use it a lot with several of my scopes. Prior to that, around twenty years ago, I hade a Vixen alt-az mount that I liked a lot. It was much better than the Custom, but not as good as the Porta. It was called the ‘Custom-D’. Here’s a picture of the Custom-D with no scope. I used to regularly use a 102mm F7 refractor on my Vixen Custom-D mount.
I also use the Porta II with my classic scopes (probably because of Terra!). It's just so easy to set up, and 60-8omm scopes ride well on it. Heck, in a pinch, I've even used 4" scopes on a Porta II, as long as the magnification isn't too high. I can't say enough about this mount. It is really the only one I use. It holds my Tak, my TV, my classic 60s, my old Celestron Vixen 80mm achro. The only other mount I really use is the Orion tripod I have set up with an AT60. Even the Vixen Polaris is put away because I don't use a 100 refractor anymore, preferring the ease of the MAK on the moon.
The ONLY original mounts I use, classics wise, are the Unitrons, because they are beautiful, but mainly because they are functional. They--just--work. Always. And these are Alt Az mounts.
You can set up a Tasco 7TE with it's original mount, and it will be fine. But you will soon find, if you are like me, that for space and functionality, if you have a Porta II and some 60mm rings and dove, using your Tasco on a Porta II will be a pleasure. I can't emphasize that enough. It will be a rock steady, easy peasy experience, from set-up to take down.
(Tale of Two Porta IIs: A Vixen 70, a good modern lunar scope, and classic Tasco 60mm.)