Concatenation in where clause

I have 2 tables and each table has say 1 column with thousands of rows.

create table #t1 (id varchar (2) )
create table #t2 (id varchar (2) )

insert into #t1 values('01')
insert into #t1 values('2')
insert into #t2 values('1')
insert into #t2 values('02')

select * from 
#t1 as a
inner join
#t2 as b
on cast(a.id as integer) = cast(b.id as integer)

select * from 
#t1 as a
inner join
#t2 as b
on a.id = b.id  OR '0' + a.id = b.id OR a.id = '0' + b.id

both columns could have values in different format but they are same in real world. So in this example, 1 is equal to 01. To get that result, i have 2 approaches mentioned above. I need a validation of my assumption that approach without casting is the better one. I can't update data in table to avoid concatenation or casting.