As promised, a quick follow-up on the steps followed by Jorous.
The reset scenario seems to solve issues when transferring from Wifi to LTE for me, i can continue to navigate in Safari when I close my Wifi from home. Rogers LTE appears immediately. Before the reset, 3G was likely to appear first, from my living room...
Another variation of this scenario might be the fact that when I installed my new iPad, it was a restore of my former iPad 2. Thus we can easily imagine the the inherited network settings might be slightly different.
When anyone tries to diagnose a problem in a thread, many "flavors" of the problem can appear, like here we would have some people with "new" new iPad and others, like my case, with "migrated" new iPad.
This discussion was very helpful, indeed, thanks to everybody... I will walk away of this thread for now and unsubscribe.