Network Question

[king1]

generally yes setting the ssid and wifi key the same does work, have done that a few times before... but there are usually gotchas, for example newer modems will often have wifi set to WPA2 only by default (for security), so for older device compatibility wpa/wpa2 needs to be changed in the modem. and sometimes you get the odd device that refuses to connect and needs to 'forgotten' and reconnected.

The other thing I usually do is set the IP range to the same subnet if its different, that way you don't need to change any static IP's.  The thompson I assume is spark, had an IP of x.x.x.254 iirc, whereas pretty much everyone else uses x.x.x.1 for the gateway. 
So either need to change the new modem ip to that as well, or simply restart all devices to pick up the new settings (BUT static IP devices will need the gateway address changed manually)

The one thing you usually need to do to the new modem is add in any port forwardings you may have

You should also benefit from better wifi - if i'm not mistaken the thomson wifi was 802.11g, since then we have had N and now AC and just trickling in is AX.  New modem will probably be 802.11AC I would think.  Wifi is still generally crap for coping large files around though.

also a decent benefit you will get (and limitation of adsl) is the greater than 1mbps upstream speed.  Often the 4G (esp. if out of town) might only get similar downstream speeds (15-20+) But on a bad day they usually get you at least 5-10mbps upstream as well. 

Downside is usually higher latency - 50ms plus pings aren't unusual...  and I have seen some due to tower locations etc who were only getting 3/1 ish, but at that level it is often cutting in and out (they really shouldn't have changed to it)..

HTH