Again, go with what a group agrees with, if using Thaumaturgy works for a group, fine, if it doesn't, don't. As long as a group follows their interpretation consistently it will most likely be okay. However, going between different groups could be a issue.
For those attempting to follow the RAW strictly, YS253 does state that Counterspell is an Evocation effect.
...so an Thaumaturgical equivalent should be possible, as long as one can get a symbolic link to the energy of the spell (as it is that which is being attacked here).
I see no real difference in a Counterspell based on Evocation or Thaumaturgy, really. The benefits of a Thaumaturgical counterspell would be that more powerful ongoing effects can be targeted more safely and that the caster do not have to have a line of sight to the target (and some "targets", like a curse, would be impossible to get a line of sight to... 
. The drawbacks are of course time and the need for symbolic links.
There are two issues here from the way I see things.
The first is that a Counterspell per RAW requires two things, and a third is suggested. The practioner needs to summon power for the Counterspell using Conviction, and use Discipline to Control that power. It is also suggested that Lore be used to assess the spell being countered to determine how much power is needed to Counterspell it, since too little means nothing changes, and too much power could result in Fallout or Backlash. There is no mention of any need for symbolic links or anything else, all a practioner needs is to be able to summon and control enough power to meet or beat the target of the Counterspell.
Now for the second issue. Thaumaturgy works and is cast differently than Evocation. The way I usually work it, is to have the player decide what sort of effect(s) they want the working to have, and use that to determine the level of Complexity for the ritual. The character then uses its Lore skill, any appropriate Aspects with Fate points, creates new temporary Aspects to Tag, and skips scenes until there is sufficient Complexity to cast the desired ritual. Once the Complexity is out of the way, the character then uses Conviction to draw shifts of power each turn, while making Discipline checks to make sure that the power drawn on any given turn is controlled. Once sufficient power has been drawn (without having the spell blow up) the ritual is cast. Depending on the Complexity of a particular working, and the Conviction, Discipline and Lore skills of the practioner, such a ritual could be cast as quickly as a minute, or it could require days, weeks or even months of preparation...
From YS253, there is no mention of any Complexity involved, it is just a straight up immediate disruption of the energy within a spell which has already been cast. One could certainly use the Thaumaturgy rules to create a ritual to cancel out or dispel an existing ritual working with a duration, but I don't see a feasible way of using Thaumaturgy to counter/cancel Evocation. Given that time exchanges used for Evocation start at Instant, and a fight using Evocation would usually last less than a minute even though it could have multiple exchanges, while the time increment for Thaumaturgy generally starts at A Minute and goes up from there.
As I read the rules, an Evocation Counterspell can't be cast to counter a direct effect (like an attack) - only an effect with a duration (like a Maneuver or a Block) can be countered. So the spell with a duration has already "gone off" when the caster tries to cast the Counterspell - I can't see that a Wizard can Counterspell an Evocation as it being cast.
So if an ongoing effects from a Thaumaturgical ritual of 10 shifts (lasting, say an afternoon) is hit by a 10 shift Counterspell (based on Evocation or, if allowed, Thaumaturgy), the effect of the ritual will be stopped for one exchange and then resumed? That is not the way I read the rules. If that was the case, a Counterspell is useless, and must be re-cast every exchange.
Actuall, the example on YS253 says that if the Counterspell succeeds, the effects of the ongoing spell is gone (not stopped, to be resumed)
Regarding an effect being Counterspelled and then resuming, the third sentence under the Counterspell heading on YS253 reads:
While such an attempt may only be temporary, it can buy the wizard precious time.
What that says to me is than an effect can be negated, briefly perhaps, and then end up resuming once someone is no longer actively Counterspelling the effect.
Going further with this explanation, the example in YS has Harry Counterspelling an Evocation (or possibly Evocation-based Sponsored Magic) cast by a Denarian. In this instance, unless the Denarian had spent shifts to sustain the Evocation, once Harry successfully Counterspelled it, the Evocation would just wink out.
This is of particular importance with respect to Wards and other long-duration castings which can have extended durations and special conditions like Wardflames and keyed links which increase the overall difficulty of the spell, but don't add directly to the defensive power of the spell.
-Cheers
