Depends what the premise of the question really is. As has been mentioned, there is no rational basis to "compete" with Thorpe, and I would argue that the micro environment that is the UK industry as a whole does not really lend itself to the concept of traditional market competitive forces that much. Of course this is highly debatable, but looking at geographical and demographical factors, I would argue they are competing first and foremost with other kinds of leisure activities within the country, and secondarily competing with foreign trips outside of it.
So personally, I would say this is more about market positioning to actually avoid direct competition, even extending to parks outside of the Merlin estate. The slice of the pie is the dwindling amount of disposable income people have to spend on leisure activities, so a park like Alton Towers needs to have a compelling enough offer to convince you to visit them as opposed to spending your money on other cheaper or more expensive alternatives. The cheaper alternatives could include a day out to somewhere else other than a theme park like a zoo or a weekend at Butlins, the more expensive alternatives could include visiting DLP or choosing another kind of holiday entirely. Trying to one-up BPB or Paultons for example, just to try and hoover up a handful of Lancashire or Hampshire residents respectively, would just be a poor investment choice and would be a gross oversimplification of the market forces effecting the domestic leisure industry. This is not really a traditional style competition industry wide, let alone among parks operated by the same company that offers a variety of annual pass products aimed at getting consumers to visit both. If Brake Run: The Ride is successful, it'll not only help Towers in terms of MAP sales, but I'd also argue it would benefit the UK industry as a whole by attracting interest in it.
Furthermore, even if this was about the need to 'compete', this question assumes that it's purely based on rollercoasters, and more simply, the height of them. As we know, there's far more to a theme park than just coasters, and there's far more to the coasters themselves than just the height of them. Although Tower's offering as a park beyond headline coasters has dwindled as a whole since the early 2000's (flat rides, family attractions, food, entertainment), it's market position is still different to Thorpe. It's certainly different enough when you consider it's geographical location. They're different parks that still do have a different enough target audience. Again, this is market positioning, not competition or a race to the clouds.
If however you are asking how can Towers build a compelling attraction after Brake Run: The Ride opens with it's signature height record, there's a number of ways they can do this, whether it's building coaster or non-coaster attraction or not.