Great question mate, I'll answer as truthfully and as honestly...

Great question mate, I'll answer as truthfully and as honestly as I can.
Your right about TLS's competitive advantage and with the latest ACCC TPG vodafone merger being blocked, it only strengthened their position. My TLS shares are up over 20% YTD.

In terms of competitor advantage and online sales vs VTG, if you're referring to purchasing the handset outright, and then walking into a Telstra store to get the plan then that is a BYO (bring your own device) plan. However, if you don't have a handset, TLS, vodafone, optus all follow the same formula that it works out better (cheaper) to get your handset on a plan (known as a MRO, mobile repayment option) as opposed to purchasing outright.
Lets say you have a $1200 handset to buy outright, but if you sign up for a 24 month plan (mro), will cost you $20 a month (contract being 24 months) which in total is $480. so you've saved money on what is virtually an interest free loan. Now, lets say after talking to the sales consultant he discovered that you actually needed a bigger plan, this will reduce the MRO payments further. (which is evidenced on the telstra website) So lets say the plan increases by $20 per month, but you get more calls, data, international calls etc, but your MRO handset device payment actually decreases by another $10 a month. You're saving money again.

Then, the sales consultant upon further conversations, discovers that you actually don't need the specific handset you were after and recommends a different one, with the same functions and same specs, but is cheaper (but also has a higher margin for VTG), then you have saved even more, while VTG have made more money by upselling the plan, resulting in higher REM's, and selling you a higher margin handset that you're happy with.

The competitive advantage I see here is you save money, have the customer facing and service, the high level of sales staff knowledge to sell you the correct device, and the convenience of being able to go back if something goes wrong. As opposed to purchasing online, having no after support, paying for shipping in case of warranty, delay of responses etc. (it's a lot easier to hold someone accountable face to face than it is online)

Unless a phone the consumer was chasing sold online for an extremely good price (which would have to well and truly be below cost price, or is second hand, I personally see no benefits of purchasing outright. as Once the MRO contract is up you own the handset regardless, can sell it secondhand or trade it in and upgrade to a new device plan, keep the same number.

And even if the consumer did buy the handset online, and then walked into a VTG store to get the plan, that is still great news, as it gives the sale consultant the opportunity to sell them sprout cases, check their home internet connection and further up sell them.

I hope that helps answers your question.

That's just my viewpoint, summarised as quickly as I could. I could go way more in depth, but I don't want to hijack the forum.